nazi is the abbreviation of nationalsozialist.
the first two syllables sound like nah-tzee, written nazi in german.
the change from DAP to NSDAP was a rebranding, copying the austrian DNSAP, which did the same in 1918.
the NSDAP even used a lot of the program points of the austrian party for their 25-Punkte-Programm.
a lot of disagreement herrschte within the NSDAP about the interpretation of national sozialismus or nationalsozialismus (e.g. should it be written in one word OR two words), the implementation of the program, the weighting of nationalism and socialism, the rhetoric, the aussendarstellung to get votes etc.
the history of the NSDAP in their long and bumpy road to power is very interesting. you would not understand it.
what counts is what the NSDAP did when in power:
it killed first the left wing of the german political system, forced the right wing into cooperation (did not need too much force, btw), then they killed the left "left" wing of itself. then more killing fueled by propaganda about german exceptionalism and inferiority of other races and nations.
do i have to wait until rocky part 1940 is made, or will you be able to look up roman numerals by yourself?